What are G-d's names?

The common consensus amongst the earliest Halachic authorities is that there are seven "holy names" which due to their holiness "may not be erased." The question remains which of G-d's names are these? To be more specific, there are many ways to write G-d's names -- which seven are root names, and which are merely derivatives of these.

The arguments revolve around the following names:

• The Tetragrammaton (YHVH)

• Adonai

• El

• Eloha

• Elohim

• Elohei

• Elohecha

• Eloheichem

• Shaddai

• Tzivaos

• Eheye asher Eheye

All these names must be treated with proper respect -- whether they are of the seven root names, or just derivatives. When in written form they must be disposed of in a dignified manner (see What's the proper way to dispose of holy objects?), and they must never be uttered in vain.